For the answer span scoring technique of [1]}, we defined \(\delta = \frac{\gamma }{\beta }\)  and performed a three-step grid search on \(\beta \)  and \(\delta \)  (i.e., the weight for the retriever score becomes \(\gamma = \beta \cdot \delta \) ).
We started with step size \(0.2\)  for both \(\beta \)  and \(\delta \)  and found the optimal pair of values \(\beta _{\textrm {1}}, \delta _{\textrm {1}}\) .
We then repeated this process with step size \(0.05\)  and then \(0.01\)  in a smaller range around the optimal \(\beta _i\)  and \(\delta _i\)  from the previous pass.
